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Infinitesimal weak symmetries, of nonlinear differential equations in two independent variables

A V Dzhamay and E M Vorob'ev

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Non-classical infinitesimal weak symmetries of PDE introduced by Olver and Rosenau (1987) are analysed. In the case of PDE in two independent variables, it is demonstrated that obtaining such symmetries is equivalent to obtaining the two-dimensional modules of non-classical partial symmetries. The Boussinesq and the nonlinear heat equations are treated from the point of view of non-classical symmetries.


PACS

02.30.Jr Partial differential equations

02.20.-a Group theory

MSC

35K05 Heat equation

35L75 Nonlinear hyperbolic PDE of higher (2) order

22Exx Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90)

Subjects

Mathematical physics

Dates

Issue 16 (21 August 1994)



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